How do you differentiate $f(x) =2xcos x$ ?

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Answer 1 · 2016-01-24T23:47:22

$f'(x)=2(cosx-xsinx)$

Use the product rule, which states that the derivative of a product of functions, like $f(x)=g(x)h(x)$ , is

$f'(x)=g'(x)h(x)+g(x)h'(x)$

Here, we have

$g(x)=2x$
$h(x)=cosx$

The derivatives of each of these are

$g'(x)=2$
$h'(x)=-sinx$

Plug these both back in to find $f'(x)$ .

$f'(x)=2(cosx)+2x(-sinx)$

Which can be simplified to be

$f'(x)=2(cosx-xsinx)$

How do you differentiate f(x) =2xcos x f(x) =2xcos x ?